SIMPLE-type preconditioners for cell-centered, colocated finite volume discretization of incompressible Reynolds-averaged Navier–Stokes equations


Correspondence to: C. M. Klaij, Maritime Research Institute Netherlands, P.O.Box 28, 6700AA Wageningen, The Netherlands.



This paper contains a comparison of four SIMPLE-type methods used as solver and as preconditioner for the iterative solution of the (Reynolds-averaged) Navier–Stokes equations, discretized with a finite volume method for cell-centered, colocated variables on unstructured grids. A matrix-free implementation is presented, and special attention is given to the treatment of the stabilization matrix to maintain a compact stencil suitable for unstructured grids. We find SIMPLER preconditioning to be robust and efficient for academic test cases and industrial test cases. Compared with the classical SIMPLE solver, SIMPLER preconditioning reduces the number of nonlinear iterations by a factor 5–20 and the CPU time by a factor 2–5 depending on the case. The flow around a ship hull at Reynolds number 2E9, for example, on a grid with cell aspect ratio up to 1:1E6, can be computed in 3 instead of 15 h.Copyright © 2012 John Wiley & Sons, Ltd.